The Dubai Shopping Festival is celebrated every year for a month to improve sales. An electronic store wants to stock computers of a specific type for the forthcoming Festival. Based on the previous year’s Festival, which lasted 32 days, the store constructed a demand distribution for the sales.

Computers sold per day Number of days Relative frequency (probability)

10 2 .1250 20 10 .3125 30 15 .5000 40 5 .0625 Each computer costs Dh 5,500 and sells at Dh 7,000. A supplier replenishes its stock every day before the store starts its business. When the random demand exceeds the available stock, there is a shortage of computers. In contrast, if the demand is less than the available stock, there will be some unsold computers. If there is a shortage, customers who do not get their computers receive a Dh 200 coupon, which can be redeemed at the store during the Festival period. Every sold computer generates a revenue of Dh 1,500 (= 7,000 − 5,500). The profit for a day is calculated from the revenue from sold computers and the shortage cost, ignoring coupon redemption. For example, a random demand of 40 computers with a stock of 25 generates a revenue of Dh 37,500, incurs a shortage cost of Dh 3,000, and earns a profit of Dh 34,500.

a. Simulate demand scenarios for 32 days of demand.

b. Estimate the potential profits of the store for the Festival season.

c. Determine the total shortage cost.

d. Determine the service level.

e. Does the store need to change its current policy of stocking 25 computers each day?

 LO.1